Rewrite as a simplified fraction. ${3.6\overline{4} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 364.4444...\\ 10x &= 36.4444...\end{align*}}$ Subtracting the two equations, we have: ${90x = 328}$ ${x = \dfrac{328}{90}} $ ${x = \dfrac{164}{45}} \text{or} {3 \dfrac{29}{45}}$